Integral Calculus: Multiple Integrals: Definition, Evaluation of double and triple integrals, evaluation of double integrals by change of order of integration, changing into polar coordinates. Applications to find Area and Volume by double integral. Beta and Gamma functions: Definitions, properties, relation between Beta and Gamma functions.

Ordinary Differential Equations of Higher Order: Higher-order ordinary differential equations with constant coefficients, homogeneous and nonhomogeneous equations-e ax, sin(ax+b), cos(ax+b), xn only, Method of variation of parameters, Cauchy’s and Legendre’s homogeneous differential equations. Applications: mass spring model.

Vector Calculus: Scalar and vector fields. Gradient, directional derivative, divergence and curl-physical interpretation, solenoidal vector fields, irrotational vector fields and scalar potential. Vector Integration: Line integrals, work done by a force and flux. Statement of Green’s theorem and Stoke’s theorem and problems without verifications.

Numerical Methods- 1: Solution of algebraic and transcendental equations: Regula-Falsi and Newton-Raphson methods. Interpolation: Finite differences, Interpolation using Newton’s forward and backward difference formulae, Newton’s divided difference formula and Lagrange’s interpolation formula. Numerical integration: Trapezoidal, Simpson’s1/3rd and 3/8thrules.

Numerical Methods– 2: Numerical solution of ordinary differential equations of first order and first degree: Taylor’s series method, Modified Euler’s method, Runge-Kutta method of fourth order, Milne’s predictorcorrector formula and Adams-Bashforth predictor-corrector method.